Abstract

Alternative theorems have proved to be important in deriving key results in optimization theory like the existence of Lagrange multipliers, duality results, scalarization of vector functions, etc. Since the pioneering result due to Julius Farkas in 1902 concerning his alternative lemma which is well known in linear programming, or even the elder alternative result established by Paul Gordan in 1873, many mathematicians have made a lot of effort to generalize both results in a nonlinear setting. To these author’s knowledge the first Gordan type result for convex functions is due to Fan et al. [13] and was established in 1957.